Q: If a student’s reading speed is at the 90th percentile of a normal distribution with mean 125 words per minute and standard deviation 24, which of the following is closest to their reading speed?

$$125 + 1.28 \times 24 \approx 155.7$$ words per minute

Question 1

Which of the following statements about the normal curve is TRUE?

Accepted Answer

The area under the normal curve is always equal to 1.

Question 2

Given a normal distribution with mean $$\mu = 0$$ and standard deviation $$\sigma = 1$$, what is the probability that a randomly selected value falls between $$z = -1$$ and $$z = 1$$?

Accepted Answer

Approximately 68%

Question 3

What is the formula for the z-score of a value $$x in a $$normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x-\mu}{\sigma}$$

Question 4

If the mean birth weight of full-term babies is 3400 grams with a standard deviation of 505 grams, what is the z-score for a baby weighing 3905 grams?

Accepted Answer

$$z = \frac{3905-3400}{505} \approx 1.0$$

Question 5

According to the Empirical Rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 6

A normal distribution has mean $$\mu = 21.8 cm $$and standard deviation $$\sigma = 2.0 cm. $$What is the probability that a randomly selected 4-year-old male has an upper arm length less than 19.8 cm?

Accepted Answer

About 16% (since $$z = -1)$$

Question 7

Which of the following is NOT a property of the normal curve?

Accepted Answer

It is skewed to the right.

Question 8

If a student’s reading speed is at the 90th percentile of a normal distribution with mean 125 words per minute and standard deviation 24, which of the following is closest to their reading speed?

Accepted Answer

$$125 + 1.28 	imes 24 \approx 155.7$$ words per minute

Question 9

Which of the following best describes the area under the standard normal curve for $$z \u003e 1.5$$?

Accepted Answer

It represents the probability that a value is more than 1.5 standard deviations above the mean.

Question 10

A normal distribution is often used to model which of the following real-world scenarios?

Accepted Answer

The distribution of heights of adult women in a country.

Question 11

If $$z = 2 in a $$standard normal distribution, what percentage of the data lies below this value?

Accepted Answer

Approximately 97.5%

Question 12

Which of the following is the correct interpretation of a z-score of -2?

Accepted Answer

The value is 2 standard deviations below the mean.

Probability, Discrete and Binomial Distributions, and the Normal Curve

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